On linear equations over split-octonions Full article
| Journal |
Electronic Journal of Linear Algebra
ISSN: 1081-3810 |
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| Output data | Year: 2026, Volume: 42, Pages: 569-590 Pages count : 22 DOI: 10.13001/ela.2026.10099 | ||||
| Tags | Octonions, Split-octonions, Linear equation, Positive characteristic. | ||||
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Abstract:
Over an algebraically closed field, we describe the affine varieties of solutions to the linear equations (ax)b=canda (bx) =cover the split-octonions. We also determine the dimensions of the solution sets of arbitrary linear monomial equations in the split-octonions. Moreover, we show that if a linear monomial equation over the split-octonions with nonzero constant term has at least two solutions, then it necessarily possesses an invertible solution
Cite:
Lopatin A.
, Zubkov A.
On linear equations over split-octonions
Electronic Journal of Linear Algebra. 2026. V.42. P.569-590. DOI: 10.13001/ela.2026.10099 OpenAlex
On linear equations over split-octonions
Electronic Journal of Linear Algebra. 2026. V.42. P.569-590. DOI: 10.13001/ela.2026.10099 OpenAlex
Dates:
| Submitted: | Nov 24, 2025 |
| Accepted: | Jun 14, 2026 |
Identifiers:
| ≡ OpenAlex: | W4404407736 |